Question

Hexachlorobenzene, C 6 Cl 6 , is a solid compound that is
somewhat volatile but not very soluble in water; water is not
soluble in C 6 Cl 6 . Solid C 6 Cl 6 and liquid water are allowed to
reach equilibrium at 20°C to form a solid phase, an aqueous
phase, and a gaseous phase. The vapor pressure of pure solid
C 6 Cl 6 is 1.45 mPa at 20°C and 8.85 mPa at 40°C.

a) A sample of the equilibrium aqueous phase was removed
and the equilibrium concentration of C 6 Cl 6 was found
to be mole fraction x B = 3 * 10^-10 . What are the vapor
pressures of H2O and C 6 Cl 6 for this phase at 20°C? The
vapor pressure of pure water is 2338 Pa at 20°C.

b)C 6 Cl 6 binds to proteins. A protein is added to the
aqueous solution, and equilibrium with solid C 6 Cl 6
is established. State whether each of the following
increases, decreases, or remains unchanged compared
to part (a):
1. The vapor pressure of C 6 Cl 6 for the aqueous solution.
2. The vapor pressure of water for the aqueous solution.
3. The concentration of dissolved (free) C 6 Cl 6 in the
aqueous solution.

c)What is the mole fraction of C 6 Cl 6 in the gas phase at
equilibrium at 20°C?

d) Calculate the heat of vaporization of solid C 6 Cl 6 .

Answer 1

The vapour liqiud distribution ratio

Ki = Yi/ Xi = Mole fraction of component i in phase Y / mole fraction of component i in phase X .....(i)

Ki= Pi*/ P = Partial Vapour Pressure in phase / Pure component vapour pressure......................................(ii)

From equ (i) & (ii)

Yi/ Xi = Pi*/ P ......................................(iii)

Part a) At 20^oC,

Vapour pressure of pure C6Cl6 (P) = 1.45 mPa

Mole fraction of pure C6Cl6 (Xi)= 1 , Mole fraction of C6Cl6 in aqueous phase = 3 x 10^-10

Partial Vapour Pressure of C6Cl6 in aqueous phase = Pi = 3 x 10^-10 x 1.45 = 4.35 x 10^-10 mPa

Vapour pressure of pure H2O (P) = 2338 Pa

Mole fraction of pure H2O (Xi)= 1 , Mole fraction of H2O in aqueous phase = 1- (3 x 10^-10) = 0.999 ppm

{Mole fraction of solute + mole fraction of solvent = 1}

Partial Vapour Pressure of H2O in aqueous phase = Pi =0.999 x 2338 = 2337.9 Pa

Part b) When a protein which is reactive towards C6Cl6 is added to the aqueous solution

1. The vapor pressure of C6Cl6 in aqueous solution will remain unchanged due to its equilibrium with solid state C6Cl6. .

2. Vapor pressure of H2O decreases because addition of non volatile solute causes decrease in the vapour pressure of solvent.

3. The concentration of dissolved C6Cl6 in the aqueous solution will remain unchanged beacuse at equilibrium as soon as C6Cl6 molecules will bind with the protein, same number of C6Cl6 molecules will be relesed by Solid state C6Cl6 into aqueous phase.

Part c) Using equation (i) & (ii)

Ki = 4.35 x 10^-10 / 1.45 = 3 = mole fraction of C6Cl6 in aqueous phase / Mole fraction of C6Cl6 in gas phase

Mole fraction of C6Cl6 in gas phase = 3 x 10^-10 / 3 = 10^-10

Part d) Calculation of Heat of vaporisation of solid C6Cl6 by Clausius-Clapeyron Equation:

Given : P₁=1.45 mPa, P₂= 8.85 mPa , ΔH =Heat of Vaporization , R= 8.314, T₁= 20^oC=293.15K ,

T₂= 40^oC =313.15K

ln (8.85/1.45) = (ΔH/ 8.314) [(1/293.15)- (1/313.15)]

ln 6.103= (ΔH/ 8.314) (0.00022)

ΔH = (1.809 * 8.314 )/ 0.00022 = 68363.75 J/mol= =68.4 kJ/mol